Exact Analysis of a One-Dimensional Attractive δ-Function Fermi Gas with Arbitrary Spin Polarization

We study a one-dimensional integrable system of N spin-1/2 fermions with attractive δ-function interaction at zero temperature. The Gaudin integral equation describing the ground state with arbitrary spin polarization is solved in the form of power series. We also study the ground state energy as a function of the coupling constant and the polarization.